Methods and systems for interpreting text using intelligent glossaries

ABSTRACT

A computer implemented method and systems used to create and interpret a set of formal glossaries which refer one to the other and are intended to define precisely the terminology of a field of endeavor. Such glossaries are known as intelligent, in the sense that they allow machines to make deductions, with interaction of human actors. Once a word is defined in an intelligent glossary, all the logical consequences of the use of that word in a formal and well-formed sentence are computable. The process includes a question and answer mechanism, which applies the definitions contained in the intelligent glossaries to a given formal sentence. The methods may be applied in the development of knowledge management methods and tools that are based on semantics; for example: modeling of essential knowledge in the field based on the relevant semantics; and computer-aided human-reasoning.

This application claims priority to provisional patent application No. 60/826,513 filed Sep. 21, 2006 entitled “Methods and systems for interpreting text using intelligent glossaries”.

BACKGROUND OF THE INVENTION

The present invention provides computational methods and systems for providing terminological precision, with regards to existing knowledge management capabilities, to model essential knowledge carried by human actors in a field of endeavor, line of business, activity or domain. The highly accurate methods and systems guarantee coherence and completeness of Semantic System of Intelligent Glossaries (SSIG) and enables the development of formal automatic interpretation of glossaries by a machine, for validating these glossaries by answering formal questions. The systems and methods as disclosed herein focus on the essential knowledge carried by human actors in a domain, whose knowledge is ultimately only accessible through the specialized language used by these humans in their day-to-day work activities. By way of example, legal documents may contain numerous idioms that the average person may not understand. The systems and methods described herein would tackle this problem by providing the user with a non-ambiguous definition for key terms, identifiers and symbols that are known within the legal field and providing them to the user in traditional jargon or language.

Several approaches to the concept of definition exist, based on mathematical, logical or data processing practices such as:

-   -   Providing a shortened but equivalent linguistic construction by         mechanisms of abbreviation and acronym;     -   Using a meaningful mathematical or logical symbol equivalent to         a term, which guarantees 100% identification of that term in any         text in a natural language;     -   Enumerating the properties of an object or a concept to be         defined;     -   Separating two complementary aspects of an object or a concept         to be defined:         -   1. “Black Box” perspective (inputs, outputs); and         -   2. “White Box” perspective (with exhaustive enumeration of             the content of the Box).     -   Studying linguistic relations like synonymy, antonymy, hyponymy         and hyperonymy to build semantic nets of word meanings.

Existing technologies including Description logics, Ontology, and Fuzzy logic are used to automate terminology. Currently, these technologies are not generally accessible and remain the province of computational linguistic specialists and researchers.

Description logics and ontology is the current state of the art. The purpose of ontology is to create a representation of the world, as well as the rules for combining representation elements to define ontological extensions. Such methods use first-order logic and set theory for knowledge modeling. For all practical purposes, Description logics defines concepts and the relations between these concepts. In this approach, what is described is necessarily a set; set inclusion is the basic mechanism for inferring knowledge and ontological extensions; concepts are modeled as subsets of elements of the universe of discourse. An Ontology classifies concepts in accordance with the inclusion relation, which is well adapted to the definition of the vocabulary of a hierarchical environment (nomenclature). Ontology is a centralized data base for sharing knowledge; but there is no formal language for solving interpretation issues between two different ontology knowledge bases. As a result, Description logics is limited given the complexity of natural languages, which can refer to a variety of concepts and documents that are produced in a dynamic and decentralized way.

Fuzzy logic uses a translation mechanism of natural language sentences into a generalized language of numerical constraints. For example, in the sentence “almost all Swedes are tall”, the word almost means 80%, while the remainder of the sentence “all Swedes are tall” is a statement, which can be formalized as a constraint. This theory is ambitious; it tackles real problems and covers a vast array of concepts, but it is still under development.

Practices currently used to address terminology include lexicons, glossaries and dictionaries. A lexicon is a list of words, symbols or identifiers dedicated to a field of endeavor. A word, symbol or identifier listed in a lexicon is called a lexical element. A glossary is a document encompassing the definitions of the lexical elements included in a lexicon. Therefore, a glossary is not a dictionary, because it does not include the definitions of all the possible meanings of the same word; on the contrary, a glossary shows only the meaning agreed upon for a specific field.

Throughout the practice of generalizing and formalizing glossaries, the Essential Knowledge dilemma arises between: size of lexicon, on the one hand, and precision of words in natural language, on the other hand; in essence: If the concept of words with multiple meanings found in natural language is fully addressed, then much knowledge on a vast number of topics can be expressed. However, it requires a massive amount of documentation that remains vague and therefore not usable by a machine; If the word meaning is restricted and specified by using a formalized language, then a very precise, focused knowledge can be expressed. However, it is ultimately purely symbolic and machine readable; but it is only understood by experts in the field and in the formal language used; moreover, this no longer provides a useful global vision of the field.

Existing knowledge management methods and technologies do not address the Essential Knowledge dilemma and many questions arise: where to stop, given the combinatorial explosion of any terminology (to define a word, it is necessary to use other words)? What is really represented with each word? How is ambiguity eliminated in the meanings? The present invention was developed to help users solve these problems and the Essential Knowledge dilemma.

The present invention applies Laws of Form (LoF), a mathematical theory created by George Spencer Brown, to lexical semantics; LoF is both a mental calculus (the Calculation of Distinctions), and a formal planar system (the Calculus of Indications). The LoF Calculation of Distinctions constrains the knowledge manager to conduct a comprehensive up-front Distinction-Based Reasoning (DBR), before writing a definition in a glossary; the LoF Calculus of Indications is used for computing formal meaningful values, i.e. the value of meaning of formal sentences, imbedding words and other lexical elements, which result from DBR analysis.

The present invention formalizes the glossary practice up to the capability of self-reference, i.e. the capability of formal self-definition, is reached; the present computer implemented method can then be re-used to formalize:

-   -   the syntax of alphabet, formulas and instructions authorized;     -   the application of a set of instructions to a formula;     -   the interpretation of the application of a set of instructions;         and     -   the computation of the answer to a question, by interpretation         of the application of a set of instructions to the question         considered as a formula.

The present invention treats words as first class citizens—i.e. as numbers or other mathematical beings—which solves the previously described:

-   1. limit of ontology for describing non-numerical meaning, while     being fully consistent with existing definitions of numbers, sets     and first order logical languages; -   2. basics of terminological precision, by producing intelligent     glossaries, which are formal glossaries certified in accordance with     the semantic interpretation of the process itself using the     self-reference capability; -   3. size of lexicon and precision of words by eliminating all     computable meanings (compound words, opposite words, union of words,     words hyponymy, . . . ).     The present invention allows automatic generation of a Minimal     Lexicon from an Intelligent Glossary; such a lexicon is the smaller     set of words for delimiting the field of endeavor of that glossary,     which solves the Essential Knowledge dilemma.

SUMMARY OF THE INVENTION

The present invention relates generally to systems and methods for knowledge management in a field based on the relevant semantics, by definition of words' meaning as precisely as numbers or other mathematical objects; and particularly to systems and methods for: knowledge modeling, computer aided translations, intelligent Web research, and computer-aided human-reasoning.

According to one embodiment, a computer implemented method of determining the meaning of formal language constructs occurring in written texts is disclosed. The method comprising the steps of: providing an Alphabet and a set of Symbols for constructing Lexical Elements, and Syntactic Elements built on the Alphabet, Lexical Elements, and Symbols; determining a Sort of Value, an Arity, a Notation, and a Type for each Syntactic Element, to provide Well-Formed Syntactic Elements and meaningless syntactic elements; building Formal Definitions from the typed Well-Formed Syntactic Elements, and determining a type for each definition to provide a list of Terminologies, Assertions, Theorems, Questions and answers; building Formal Glossaries as ordered sets of Formal Definitions; providing to an actor at least one Formal Glossary, and a related Minimal Lexicon; parsing, verifying and normalizing each Formal Definition from the Formal Glossary, to provide a list of Defined Lexical Elements and undefined lexical elements; allowing the actor to refer, search, cluster or select written texts, from the Defined Lexical Elements contained within Minimal Lexicons and appearing within the written texts; acquiring questions from the actor, wherein each question is a set of formal texts containing at least one Well-Formed Syntactic Element; parsing, verifying and normalizing each Well-Formed Syntactic Element in questions; retrieving, for each Defined Lexical Element contained within questions, all the applicable Formal Definitions from the Formal Glossary; applying Formal Definitions to Defined Lexical Elements in the questions in accordance with an interpretation process having at least one critical algorithm; providing values to the actor; coding each question and its meaningful value as a new Questions and answers definition; and saving the new Questions and answers definitions in the Formal Glossary, which turns the Formal Glossary into a new Intelligent Glossary.

According to another embodiment of the present invention is disclosed. A computer implemented method of determining the meaning of formal language constructs occurring in written texts, the method comprising the steps of: providing an Alphabet and a set of Symbols for constructing Lexical Elements, and Syntactic Elements built on the Alphabet, Lexical Elements, and Symbols; determining a Sort of Value, an Arity, a Notation, and a Type for each the Syntactic Element, to provide Well-Formed Syntactic Elements and meaningless syntactic elements; building Formal Definitions from the typed Well-Formed Syntactic Elements, and determining a type for each definition to provide a list of Terminologies, Assertions, Theorems, Questions and answers; and building Formal Glossaries as ordered sets of Formal Definitions; acquiring from a Knowledge Manager a Formal Glossary content; parsing, verifying and normalizing each Formal Definition contained in the Formal Glossary, to provide a list of Defined Lexical Elements and undefined lexical elements; drawing consequences of each Assertion and Theorem of the Formal Glossary, to compute new derived Assertions and to check compliance with existing Terminologies, in accordance with an interpretation process having at least one critical algorithm; acquiring questions from an actor, wherein each the question is a set of formal texts containing at least one Well-Formed Syntactic Element; parsing, verifying and normalizing each Well-Formed Syntactic Element in the question; retrieving, for each Defined Lexical Element contained within the questions, all the applicable Formal Definitions from the Formal Glossary; applying the Formal Definitions to the Defined Lexical Elements in the questions in accordance with an interpretation process having at least one critical algorithm; providing the values to the actor; coding each question and its meaningful value as a new Question & answer definition; processing a Formal Glossary as a set of formal texts, using the self-reference capacity of the present computer implemented method, to certify the Formal Glossary; and saving the certified Formal Glossary and its related Minimal Lexicon, wherein the lexicon is comprised of at least one Well-Defined Lexical Element, as an initial Intelligent Glossary.

An Interpretation System for verifying, implementing and using a Semantic System of Intelligent Glossaries, the system comprising at least: an interpretation module having an initialization module, at least one critical algorithm, wherein the interpretation module provides a value for questions, which are set of formal texts containing at least one Well-Formed Syntactical Element; a Parsing module which processes texts of formal glossaries and formal questions; an Add Definition module for verifying a formal glossary, definition by definition, and for certifying compliance and consistency of the glossary; at least one active glossary for storing current glossaries of the whole system; a current substitution initialized with the empty set and updated after each translation; a Rewriting Area for computing on formulas, from the initial formal text of a question, up to its meaningful value; a Words Table, for storing natural language words and the name of their container glossary; a viewer module for editing glossaries and questions, and for interacting with actors; and a File update module for updating glossaries having at least one definition and associated interpretation from the interpretation module.

These and other features, aspects and advantages of the present invention will become better understood with reference to the following drawings, description and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts the Synopsis of a Semantic System of Intelligent Glossaries (SSIG) according to the present invention;

FIG. 2 depicts the Internal Structure of the SSIG Interpretation System and an Overview of mains modules according to the present invention;

FIG. 3 depicts Model Elements—Data & Processes;

FIG. 4 depicts a Knowledge Management System based on a SSIG;

FIG. 5 depicts the notations used for describing algorithms.

FIG. 6 depicts the Formula Calculation Algorithm (FCA);

FIG. 7 depicts the Add Definition Algorithm (ADA); and the Equation Resolution Algorithm (ERA).

DETAILED DESCRIPTION OF THE INVENTION

The following detailed description is of the best currently contemplated modes of carrying out the invention. The description is not to be taken in a limiting sense, but is made merely for the purpose of illustrating the general principles of the invention, since the scope of the invention is best defined by the appended claims.

The computer-implemented method uses the Laws of Form (LoF) Calculus of Indications, a mathematical theory created by George Spencer Brown, for computing on the forms resulting from distinctions made by human actors; forms represent words meaning. The LoF Calculus of Indications is a pure formal system and would be appreciated by those with skill in the art. In accordance with the LoF Convention of intention: the intent of a symbol or chain of symbols is limited to the use allowed to it; in other words, what is not allowed is forbidden. The LoF Calculus of Indications brings both Arithmetic Laws and Algebraic Initials that support several mathematical interpretations:

1. Boolean logics:

-   -   LoF Calculus of Indications was initially interpreted for         Boolean logics by George Spencer Brown;     -   Boolean logics is used for computing the truth value of Formal         declarative sentences;

2. Ternary logics:

-   -   LoF Calculus of Indications was extended by Francisco Varela to         introduce a third Truth Value, to encompass the occurrence of         self-referential situations, which entails the abandonment of         the Law of excluded middle;     -   Ternary logics is used for computing the truth value of formal         interrogative sentences; and for processing cycles of         computation;

3. Bunch Theory:

-   -   LoF provides an arithmetic to Bunch Theory developed by         Eric C. R. Hehner; a bunch is not a set: a bunch is an unordered         and unpackaged collection of elements, which allows duplication         of elements; bunches are used to define sets by their content;     -   Bunch Theory is used for computing the multiple reality values         of formal naming sentences;

4. Category Theory:

-   -   LoF Calculus of Indications extended to Bunch Theory can itself         be extended to encompass the Category Theory, which was         introduced by Eilenberg & Mac Lane to formalize transformations         between mathematical objects sharing the same structure;     -   Category Theory is used for computing upon changing values         (either truth or reality values) of formal functional sentences;         and to formalize the computation process itself.

The computer-implemented method uses Arithmetic and Algebraic Mechanisms, together with the LoF Calculus of Indications; in the present document, the following algebraic notations are used:

-   -   the Greek Letters (α, β, γ, δ, φ, κ, η, ω, υ, σ, . . . ) refer         to any symbol or chain of symbols;     -   The formal Arithmetic and Algebraic writings are:         -   Packaging a symbol or a chain of symbols is writing it with             a left “[” on its left, and a right “]” on its right; for             example:             -   Packaging the chain of symbols “me” is writing the                 Package “[me]”;         -   Calling 2 symbols or chains of symbols is writing them             separated by a space; for example:             -   Calling the 2 chains of symbols, “me” and “too”, is                 writing the Call “me too”;         -   Changing a symbol or chain of symbols into another symbol or             chains of symbols, is writing them separated by a “             ” (Rightwards Wave Arrow):             -   “                 ” stands for the words “is changed to”, i.e. “α                 β” means “α is changed to β”;             -   the arrow indicates the direction of the change: α is                 the source; β is the target;         -   Rewriting a symbol or a chain of symbols is changing it by             replacing whole or part of it, in accordance with a             Rewriting Rule; for example, a Rewriting Rule of equivalence             can be written as a 2-sides equation:             -   The left side, and the right side of that equation have                 the same value;             -   In any symbol or chain of symbols in which the left side                 of the equation appears, it can be rewritten “on the                 spot” into that symbol or chain of symbols by the right                 side of the equation, without changing the value of the                 symbol or chain of symbols.

According to one method, a computer implemented method of determining the meaning of formal language constructs occurring in written texts is provided, the method comprising the steps of: providing an Alphabet and a set of Symbols for constructing Lexical Elements, and Syntactic Elements built on the Alphabet, Lexical Elements, and Symbols; determining a Sort of Value, an Arity, a Notation, and a Type for each Syntactic Element, to provide Well-Formed Syntactic Elements and meaningless syntactic elements; building Formal Definitions from the typed Well-Formed Syntactic Elements, and determining a type for each definition to provide a list of Terminologies, Assertions, Theorems, Questions & answers; and building Formal Glossaries as ordered sets of Formal Definitions; providing to an actor at least one Formal Glossary, and its related Minimal Lexicon; parsing, verifying and normalizing each Formal Definition from the Formal Glossary, to provide a list of Defined Lexical Elements and undefined lexical elements; allowing an actor to refer, search, cluster or select written texts, from Defined Lexical Elements contained within Minimal Lexicons and appearing within the written texts; acquiring questions from an actor, wherein each question is a set of formal texts containing at least one Well-Formed Syntactic Element; parsing, verifying and normalizing each Well-Formed Syntactic Element in the questions; retrieving, for each Defined Lexical Element contained within the questions, all the applicable Formal Definitions from the Formal Glossary; applying the Formal Definitions to the Defined Lexical Elements in the questions in accordance with an interpretation process having at least one critical algorithm; providing the values to the actor; coding each question and its meaningful value as a new Questions & answers definition; and saving these new definitions in the Formal Glossary, which turns the Formal Glossary into a new Intelligent Glossary. The step of constructing Lexical and Syntactic Elements may be performed by the steps of: selecting an Alphabet containing at least Lowercase Letters, Uppercase Letters, and Digits; selecting from the set of Symbols, three Primary Symbols i.e. the symbols: “⊥”, “@” and “[ ]”; calling Primary value, a Primary Symbol used singly; calling Ordinary Symbols, all other symbols from the set of Symbols; including:—Definition Symbols, i.e. the symbols: “|−”, “≈”, and “;”; —Change Symbol, i.e.: “

” (rightwards wave arrow); —Deactivation Symbol, i.e. “‘ ’” (simple quote); —any other symbols, such as Parentheses, Linguistic symbols, Logic symbols, Arithmetic symbols, Quantifiers, and Function symbols; calling Word, a chain of Lowercase Letters, coding Natural Languages words, i.e.: nouns, adjectives, verbs, and adverbs; calling Number, a chain of digits, coding Natural whole numbers; calling Elements the group consisting of Primary values, Words, Numbers, and Arrows; calling Arrow, an Element (the target) separated from either an Element or an Arrow (the source) by a Change Symbol; calling Identifier, a chain of letters or digits beginning by an Uppercase Letter; calling Lexical Elements the group consisting of Words, Identifiers, and Ordinary Symbols; selecting Variable symbols in the group consisting of Uppercase Letters used singly; calling Syntactic Elements the group consisting of Symbols, Words, Numbers, Identifiers, Arrows, and Variables. A Notation—which is a data attribute—may be assigned to each Syntactic Element that is a Symbol, this may be performed by the steps of: assigning a Prefix Notation for a symbol that is attached to the beginning of its arguments; for example: “

” is a Prefix symbol in “

(X=X)”; assigning a Postfix Notation for a symbol that is attached at the end of its arguments; for example: “!” is a Postfix symbol in “2!”; assigning a Infix Notation for a symbol that is inserted between its arguments; for example: “+” is an Infix symbol in “2+2”; assigning a Circumfix Notation for a unary symbol that is placed around (bracketing) its arguments; for example: “[ ]” is a Circumfix symbol in “[1 2]”. The step of assigning a Sort of Value—which is a data attribute—to each Syntactic Element may be performed by steps of: selecting Sorts of Value in the group consisting of Truth-values (True, False, Unknown) and Reality-values, sub-sorted into Numerical, Non-Numerical reality; determining if that Sort of Value—Truth or Reality—is either a Fixed or Changing value; assigning a unique Sort of Value—to each Ordinary Symbol, according the usual Sort of Value of its arguments and results; for example: “+” is a Fixed Numerical Reality valued Symbol; processing Primary symbols as Syntactic Elements with polymorphic sorts, namely: used singly or with Truth-valued Syntactic Elements, they have Truth values (Fixed or Changing); used with Reality-valued Syntactic Elements, they have Reality values (Fixed or Changing). The step of assigning an Arity—which is a whole number—to each Syntactic Elements, may comprise the steps of: assigning an Arity equal to zero to Elements, Variables, and Identifiers; assigning to each Ordinary Symbol, an Arity equal to the number of authorized arguments; for example: “+” is a 2-arity Infix symbol in “2+2”; computing the Arity of Primary Symbols intangled inside or around other Syntactic Elements, in accordance with their position in regards to the Syntactic Elements, namely:—assigning an Arity equal to 1 to a Circumfix Primary symbol “[ ]”; for example: in the chain “[[ ]]”, the inner “[ ]” is a 0-arity symbol, and the outer [ ]” is a 1-arity symbol; —assigning an Arity equal to 2 to an infix Primary symbol “⊥”; for example: in (the chain “⊥⊥⊥”, the inner “⊥” is a 2-arity symbol, and the 2 outer “⊥” are 0-arity symbols. There may be the steps of assembling a unique Symbol concatenated with only 0-arity Syntactic Elements, respecting the Sort of Value, Arity and Notation of the Symbol; such a well formed syntactic element is called Atomic; for example, X+1 is atomic; a standalone Element is atomic; for example, 1 is atomic; assembling a unique Symbol concatenated with other Well-Formed Syntactic Elements, atomic or non-atomic, respecting the Sort, Arity and Notation of the unique Symbol, and using parentheses to disambiguate the order of evaluation of Syntactic Elements; such a Well-Formed Syntactic Element is called Non-atomic; calling all other forms of syntactic elements “ill-formed”, and therefore “meaningless”, as their value is not computable by the present computer implemented method; calling “the head”, the unique Symbol of a Well-Formed Syntactic Element, atomic or non-atomic, and calling “the body”, the rest of the Well-Formed Syntactic Element; the head and the body of a standalone Element are the same; calling “the Sort of Value of a Well-Formed Syntactic Element”, the Sort of Value of the head of that Well-Formed Syntactic Element; calling “bound”, an occurrence of a variable, which is in the body of a quantifier or a function symbol in a Well-Formed Syntactic Element; otherwise, the occurrence of that variable is called “free”; calling “ground”, a Well-Formed Syntactic Element which contains no free variables; otherwise it is called “non-ground”; calling “literal”, a Well-Formed Syntactic Element which contains only Elements, and Primary Symbols; otherwise it is called “non-literal”; a literal is ground. The critical algorithm utilized in the interpretation process may be the Formula Calculation Algorithm (FCA), the Add Definition Algorithm (ADA); and the Equation Resolution Algorithm (ERA).

Well-Formed Syntactic Elements may be typed as: Instructions, which contain at least one Symbol of Definition, wherein Instructions are sub-typed as: Injunctions, built on two formulas, the indicative part (the right-hand formula) and the body (the left-hand formula) surrounding the infix Symbol of Definition “≈”;

a simple Injunction is coded as “β≈γ”;

a multiple Injunction is coded as “β₀≈γ₀; β₁≈γ₁; . . . ”;

An Injunction—simple or multiple—is called:

Atomic, if all its left-hand Formulas are atomic;

Unknown, if all its right-hand Formulas are @;

Definitions, built on an expression—the pre-condition, and an injunction, simple or multiple, separated by the infix symbol of definition “|−”; a definition is coded as a three-part pattern form, namely:

-   -   “α|−β≈γ”, when constituted with a pre-condition α, and a simple         Injunction, “β≈γ”; and     -   “α|−η”, when constituted with a pre-condition α, and a multiple         Injunction, η;

A Definition is called ground, if both its pre-condition and its Injunction, simple or multiple, are ground. Glossaries, which are ordered lists of Definitions, may be separated by the infix Symbol of Definition “;”. Formulas, which contain no Symbols of Definition, may be sub-typed as Expressions (which have truth-values), and Terms (which have reality values); wherein expressions may be sub-typed as Indication Expressions (atomic) and Ordinary expressions (non-atomic); equating literal ordinary expressions either as Arrangements (with multiple Primary Symbols) or Primary values (with only one Primary Symbol); wherein Terms may be sub-typed as Indication Terms (atomic) and Ordinary Terms (non-atomic); equating literal ordinary terms either as Packages (packaged forms, single or multiple), Bunches (non-packaged and with multiple Elements) or Unitary Terms (“uniterms” with only one non-packaged Element, i.e.: numbers, words and arrows). Each Formal Definition may have a definition type selected from the group consisting of Terminologies, Assertions, Theorems and Questions & answers, wherein:

-   -   1. a Terminology is a non-ground definition with an atomic         injunction,     -   2. an Assertion or Anti-assertion is a ground definition with an         atomic injunction,     -   3. a Theorem or Anti-theorem is a non-ground definition with a         non-atomic injunction,     -   4. a Question & answer is a definition with an Unknown         injunction, which must be computed by the present computer         implemented method.         These 4 basic types of definition are further sub-typed in other         sub-types of definition in accordance with their syntactical         structure. A Defined Lexical Element is the unique lexical         element that appears within the atomic indicative part β, of a         three-part pattern Terminology definition coded as “α|−β≈γ”.

The method may comprise the steps of providing to an Actor at least one Intelligent Glossary; parsing and verifying the Formal Glossaries and their Formal Definitions to infer the type of Syntactic Elements they contain; ordering and storing the Formal Definitions from the Formal Glossaries. There may also be the steps of: producing a Minimal Lexicon build from Defined Lexical Elements that appear in the indicative part β of a definition ‘α|−β≈γ’ in the Formal Glossary. The method may further comprise the steps of allowing an actor to cluster or select written texts from Lexical Elements contained within Minimal Lexicons and appearing within written texts, and may further comprise of the steps of: respecting field specific distinctions, as each Lexical Element contained within a Minimal Lexicon is the Indication in a Distinction, in accordance with Laws of Form Calculus of Distinctions; modularizing a field of endeavor into domains by using distinctions applicable to one domain, for drawing precise boundaries with all other domains in that field of endeavor; providing a single meaning to all natural language words, symbols and identifiers for the whole system of Minimal Lexicons, considered as sets of lexical elements, from Intelligent Glossaries; operating semantically, i.e. preserving the single meaning of elements of the Minimal Lexicon with the usual set operators (i.e. set union, set intersection, set complement, set difference, set symmetric difference, . . . ) in order to construct complex Lexicons, covering specifically the field of endeavour; selecting key-words from written texts, which are the high-frequency words appearing within the written texts in that field of endeavor; semantic researching on the Internet or Intranet by identifying key-words with Lexical Elements contained in Minimal Lexicons generated from Intelligent Glossaries of the domains. There may be the steps of accepting from an actor, human or machine, a question which is a set of formal texts containing at least one Well-Formed Syntactic Element, wherein the value of the Well-Formed Syntactic Element is unknown; parsing and verifying the formal text of the question to infer the type of Syntactic Element it contains, and to produce Formulas contained in the question; and initializing the Rewriting Area with the Formulas contained in the question. The may also be the steps of retrieving for each Formula in the Rewriting Area, all matching Formal Definitions from Formal Glossaries, using algebraic mechanisms of unification and instantiation; eliminating redundant or inconsistent matching definitions to provide an optimized tree of applicable definitions, and its related Current Substitution; building the tree of all applicable definitions from Formal Glossaries, to each sub-formula of the Formulas in the Rewriting Area.

The interpretation process may comprise the steps of: starting by translating each sub-formula of the Formulas in the Rewriting Area, in accordance with the algebraic mechanisms of substitution and replacement, and continues up to a literal Formula appears; stopping by reducing the literal Formula in the Rewriting Area, in accordance with the Laws of Form Calculus of indications for computing its normal form, which is its value; by Laws of Form, this value is unique. The step of translating a Formula may be comprising: applying Formal Definitions from the tree of all applicable definitions, to sub-formulas of the Formula in the Rewriting Area; considering Formal Definitions as conditional rewriting rules, to transform a formula while preserving its value; combining and comparing different results from the tree of all applicable definitions, to produce a unique meaningful value; coding <α> the unique value of Formula α, as computed in accordance with the present interpretation process. The step of applying Formal Definitions may be precisely defined by the sentence “Apply a Definition (α|−β≈γ) to a Formula φ”, which is the combination of the Pre-condition and Injunction mechanisms, namely:

-   -   1. If <α> is True then apply Injunction β≈γ to φ, i.e. replacing         with γ any appearance of β in φ;     -   2. If <α> is False then do nothing to φ;     -   3. If <α> is Undefined then stop current transformation of φ,         which transmit Unknownness value.         The symbol <α> may be used to indicate any predetermined         criteria.

The method may comprise the steps of inserting LoF Algebraic Initials, Position & Transposition, as Theorem type Definition in active Glossary; initializing an active Glossary with hard-coded definitions of string manipulations. The list of Hard-Coded Functions may be:

-   -   1. concatenation of a string on the right side into a string;         and updating the Current Substitution and the Rewriting Area;     -   2. de-concatenation of a string on the right side into a string,         and a character; and updating the Current Substitution and the         Rewriting Area;     -   3. concatenation of a string on the left side into a string; and         updating the Current Substitution and the Rewriting Area;     -   4. de-concatenation of a string on the left side into a string         and a character; and updating the Current Substitution and the         Rewriting Area;     -   5. generic equality of two formulas, including syntactic         equality of strings, by unifying, valuating—by using FCA, and         comparing syntactically their respective values, and updating         the Current Substitution and the Rewriting Area;     -   6. deactivation of a Well-Formed Syntactic Element, which turns         it into a mere and purely syntactical chain of symbols; and     -   7. quantification of a Formula by a variable, which develops         that quantified Formula by listing the variable on the Words         Table: “For All” Quantifier is developed as a generalized         conjunction; “There exists” Quantifier is developed as a         generalized disjunction.

The method may comprise of the step of: providing an answer to actor as the meaningful value of a syntactic element, if syntactic element is not meaningless; coding the meaningful value of a Well-Formed Syntactic Element as a question & answer type definition, on the form:

-   -   ‘[ ]|−β≈γ’, for a question without pre-condition, where β is the         formula of the question, and γ is the meaningful value;     -   ‘[ ]|−α         β≈[ ]’, for a question with a pre-condition, where α is the         pre-condition of the question, β is the formula of the question         (         is the logical implication);         saving in the formal glossary the result definition, in         accordance with the types of definition.

A computer implemented method of determining the meaning of formal language constructs occurring in written texts, the method comprising the steps of: providing an Alphabet and a set of Symbols for constructing Lexical Elements, and Syntactic Elements built on the Alphabet, Lexical Elements, and Symbols; determining a Sort of Value, an Arity, a Notation, and a Type for each the Syntactic Element, to provide Well-Formed Syntactic Elements and meaningless syntactic elements; building Formal Definitions from the typed Well-Formed Syntactic Elements, and determining a type for each definition to provide a list of Terminologies, Assertions, Theorems, Questions & answers; and building Formal Glossaries as ordered sets of Formal Definitions; acquiring from a Knowledge Manager (12) a Formal Glossary content; parsing, verifying and normalizing each Formal Definition contained in the Formal Glossary, to provide a list of Defined Lexical Elements and undefined lexical elements; drawing consequences of each Assertion and Theorem of the Formal Glossary, to compute new derived Assertions and to check compliance with existing Terminologies, in accordance with an interpretation process having at least one critical algorithm; acquiring questions from an actor, wherein each question is a set of formal texts containing at least one Well-Formed Syntactic Element; parsing, verifying and normalizing each Well-Formed Syntactic Element in the question; retrieving, for each Defined Lexical Element contained within the questions, all the applicable Formal Definitions from the Formal Glossary; applying the Formal Definitions to the Defined Lexical Elements in the questions in accordance with an interpretation process having at least one critical algorithm; providing the values to the actor; coding each question and its meaningful value as a new Question & answer definition; processing a Formal Glossary as a set of formal texts, using the self-reference capacity of the present computer implemented method, to certify the Formal Glossary; and saving the certified Formal Glossary and its related Minimal Lexicon, wherein the lexicon is comprised of at least one Well-Defined Lexical Element, as an initial Intelligent Glossary. The step of constructing Lexical and Syntactic Elements, may further comprise the steps of: selecting an Alphabet containing at least Lowercase Letters, Uppercase Letters, and Digits; selecting from the set of Symbols, three Primary Symbols i.e. the symbols: “⊥”, “@” and “[ ]”; calling Primary value, a Primary Symbol used singly; calling Ordinary Symbols, all other symbols from the set of Symbols; including:—Definition Symbols, i.e. the symbols: “|−”, “≈”, and “;”; —Change Symbol, i.e.: “

” (rightwards wave arrow); —Deactivation Symbol, i.e. “‘ ’” (simple quote); —any other symbols, such as Parentheses, Linguistic symbols, Logic symbols, Arithmetic symbols, Quantifiers, and Function symbols; calling Word, a chain of Lowercase Letters, coding Natural Languages nouns, adjectives, verbs, and adverbs; calling Number, a chain of digits, coding Natural whole numbers; calling Elements the group consisting of Primary values, Words, Numbers, and Arrows; calling Arrow, an Element (the target) separated from either an Element or an Arrow (the source) by a Change Symbol; calling Identifier, a chain of letters or digits beginning by an Uppercase Letter; calling Lexical Elements the group consisting of Words, Identifiers, and Ordinary Symbols; selecting Variable symbols in the group consisting of Uppercase Letters used singly; calling Syntactic Elements the group consisting of Symbols, Words, Numbers, Identifiers, Arrows, and Variables.

A Notation—which is a data attribute—may be assigned to each Syntactic Element that is a Symbol, further comprising the steps of:

-   -   assigning a Prefix Notation for a symbol that is attached to the         beginning of its arguments; for example: “         ” is a Prefix symbol in “         (X=X)”;     -   assigning a Postfix Notation for a symbol that is attached at         the end of its arguments; for example: “!” is a Postfix symbol         in “2!”;     -   assigning a Infix Notation for a symbol that is inserted in the         middle of its arguments; for example: “+” is an Infix symbol in         “2+2”;

assigning a Circumfix Notation for a unary symbol that is placed around (bracketing) its arguments; for example: “[ ]” is a Circumfix symbol in “[1 2]”

The method may further comprise the step of assigning a Sort of Value—which is a data attribute—to each Syntactic Element, further comprising the steps of: selecting Sorts of Value in the group consisting of Truth-values (True, False, Unknown) and Reality-values, sub-sorted into Numerical, Non-Numerical reality; determining if that Sort of Value—Truth or Reality—is either a Fixed or Changing value; assigning a unique Sort of Value—to each Ordinary Symbol, according the usual Sort of Value of its arguments and results; for example: “+” is a Fixed Numerical Reality valued Symbol; processing Primary symbols as Syntactic Elements with polymorphic sorts, namely: used singly or with Truth-valued Syntactic Elements, they have Truth values (Fixed or Changing); used with Reality-valued Syntactic Elements, they have Reality values (Fixed or Changing).

The method may comprise the step of assigning an Arity—which is a whole number—to each Syntactic Elements, further comprising the steps of: assigning an Arity equal to zero to Elements, Variables, and Identifiers; assigning to each Ordinary Symbol, an Arity equal to the number of authorized arguments; for example: “+” is a 2-arity Infix symbol in “2+2”; computing the Arity of Primary Symbols intangled inside or around other Syntactic Elements, in accordance with their position in regards to the Syntactic Elements, namely:

-   -   assigning an Arity equal to 1 to a Circumfix Primary symbol “[         ]”; for example: in the chain “[[ ]]”, the inner “[ ]” is a         0-arity symbol, and the outer [ ]” is a 1-arity symbol;     -   assigning an Arity equal to 2 to an infix Primary symbol “⊥”;         for example: in (the chain “⊥⊥⊥”, the inner “⊥” is a 2-arity         symbol, and the 2 outer “⊥” are 0-arity symbols.

The method may further comprise the step of: assembling a unique Symbol concatenated with only 0-arity Syntactic Elements, respecting the Sort of Value, Arity and Notation of the Symbol; such a well formed syntactic element is called Atomic; for example, X+1 is atomic; a standalone Element is atomic; for example, 1 is atomic; assembling a unique Symbol concatenated with other Well-Formed Syntactic Elements, atomic or non-atomic, respecting the Sort, Arity and Notation of the unique Symbol; using parentheses to disambiguate the order of evaluation of Syntactic Elements; such a Well-Formed Syntactic Element is called Non-atomic; calling all other forms of syntactic elements “ill-formed”, and therefore “meaningless”, as their value is not computable by the present computer implemented method; calling “the head”, the unique Symbol of a Well-Formed Syntactic Element, atomic or non-atomic, and calling “the body”, the rest of the Well-Formed Syntactic Element; the head and the body of a standalone Element are the same; calling “the Sort of Value of a Well-Formed Syntactic Element”, the Sort of Value of the head of that Well-Formed Syntactic Element; calling “bound”, an occurrence of a variable, which is in the body of a quantifier or a function symbol in a Well-Formed Syntactic Element; otherwise, the occurrence of that variable is called “free”; calling “ground”, a Well-Formed Syntactic Element which contains no free variables; otherwise it is called “non-ground”; calling “literal”, a Well-Formed Syntactic Element which contains only Elements, and Primary Symbols; otherwise it is called “non-literal”; a literal is ground.

The Well-Formed Syntactic Elements may be typed as: Instructions, which contain at least one Symbol of Definition, wherein Instructions are sub-typed as:

-   -   Injunctions, built on two formulas, the indicative part (the         right-hand formula) and the body (the left-hand formula)         surrounding the infix Symbol of Definition “≈”;         -   a simple Injunction is coded as “β≈γ”;         -   a multiple Injunction is coded as “β₀≈γ₀; β₁≈γ₁; . . . ”;

An Injunction—simple or multiple—is called:

-   -   Atomic, if all its left-hand Formulas are atomic;     -   Unknown, if all its right-hand Formulas are @;

Definitions, built on an expression—the pre-condition, and an injunction, simple or multiple, separated by the infix symbol of definition “|−”; a definition is coded as a three-part pattern form, namely:

-   -   “α|−β≈γ”, when constituted with a pre-condition α, and a simple         Injunction, “β≈γ”; and     -   “α|−η”, when constituted with a pre-condition α, and a multiple         Injunction, η;

A Definition is called ground, if both its pre-condition and its Injunction, simple or multiple, are ground;

Glossaries, which are ordered lists of Definitions, separated by the infix Symbol of Definition “;”;

Formulas, which contain no Symbols of Definition, may be sub-typed as Expressions (which have truth-values), and Terms (which have reality values); expressions may be sub-typed as Indication Expressions (atomic) and Ordinary expressions (non-atomic); equating literal ordinary expressions either as Arrangements (with multiple Primary Symbols) or Primary values (with only one Primary Symbol); the Terms may be sub-typed as Indication Terms (atomic) and Ordinary Terms (non-atomic); equating literal ordinary terms either as Packages (packaged forms, single or multiple), Bunches (non-packaged and with multiple Elements) or Unitary Terms (“uniterms” with only one non-packaged Element, i.e.: numbers, words and arrows). Each Formal Definition may have a definition type selected from the group consisting of Terminologies, Assertions, Theorems and Questions & answers, wherein:

-   -   1. a Terminology is a non-ground definition with an atomic         injunction,     -   2. an Assertion or Anti-assertion is a ground definition with an         atomic injunction,     -   3. a Theorem or Anti-theorem is a non-ground definition with a         non-atomic injunction,     -   4. a Question & answer is a definition with an Unknown         injunction, which must be computed by the present computer         implemented method. These 4 basic types of definition are         further sub-typed in other sub-types of definition, in         accordance with their syntactical structure. A Defined Lexical         Element is the unique lexical element that appears within the         atomic indicative part β, of a three-part pattern Terminology         definition coded as “α|−β≈γ”.

The method may further comprise the steps of: acquiring and ordering from a Knowledge Manager (12) Formal Definitions having the same field specific semantic as their original Natural Language sentences; respecting the field specific distinctions, as each Defined Lexical Element results from a Laws of Form Calculus of Distinction reasoning by the Knowledge Manager (12); formalizing the Formal Definitions following a three-part pattern expressed as ‘α|−β≈γ’, where β is the indication of the underlying distinction, and defining the Defined Lexical Element. There may also be the steps of: parsing and verifying the Formal Glossaries and their Formal Definitions to infer the type of Syntactic Element they contain; normalizing Primary Expressions, for eliminating non-satisfiable sub-formulas while preserving their value, by applying repeatedly the Laws of Forms Algebraic Initials; providing a list of Defined Lexical Elements contained in the Formal Definitions; producing a Minimal Lexicon built from Defined Lexical Elements that appear in the indicative part β of a definition ‘α|−β≈γ’ in the Formal Glossary. There may also be the steps of: retrieving each Assertion and Theorem definition from the Formal Glossary; drawing consequences of each Assertion and Theorem definition, in accordance with an interpretation process having at least one critical algorithm; verifying consistency of each Assertion and Theorem definition with existing Terminology definitions, in accordance with the Laws of Form; providing new derived Assertion definitions, which are logical consequences of the Assertion and Theorem definition. The method may also have the steps of: accepting from an actor, human or machine, a question which is a set of formal texts containing at least one Well-Formed Syntactic Element, wherein the value of the Well-Formed Syntactic Element is unknown; parsing and verifying the formal text of the question to infer the type of Syntactic Element it contains, and to produce Formulas contained in the question; and initializing the Rewriting Area with the Formulas contained in the question. There may also be the steps of: retrieving for each Formula in the Rewriting Area, all matching Formal Definitions from Formal Glossaries, using algebraic mechanisms of unification and instantiation; eliminating redundant or inconsistent matching definitions to provide an optimized tree of applicable definitions, and its related Current Substitution; building the tree of all applicable definitions, acquired from Formal Glossaries, to each sub-formula of the Formulas in the Rewriting Area. There may also be the step of: providing an answer to the actor as the meaningful value of a syntactic element, if the syntactic element is not meaningless. There may also be the step of: saving the consistent ordered set of Formal Definitions, as a certified Formal Glossary. There may also be the step of: processing a certified Formal Glossary as a formal text using the self-referential Glossary coding the high level specification of the present computer implemented method; certifying the compliance of the certified Formal Glossary with the present computer implemented method; and providing an initial Intelligent Glossary, and its related Minimal Lexicon, from the certified and consistent Formal Glossary.

The interpretation process: may start by translating each sub-formula of the Formulas in the Rewriting Area, in accordance with the algebraic mechanisms of substitution and replacement, and continues up to a literal Formula appears and stop by reducing the literal Formula in the Rewriting Area, in accordance with the Laws of Form Calculus of indications for computing its normal form, which is its value; by Laws of Form, this value is unique.

The steps of translating a Formula may be: applying Formal Definitions from the tree of all applicable definitions, to sub-formulas of the Formula in the Rewriting Area; considering Formal Definitions as conditional rewriting rules, to transform a formula while preserving its value; combining and comparing different results from the tree of all applicable definitions, to produce a unique meaningful value; coding <α> the value of Formula α, as computed in accordance with the present interpretation process. Applying Formal Definitions is precisely defined by the sentence “Apply a Definition (α|−β≈γ) to a Formula φ”, which is the combination of the Pre-condition and Injunction mechanisms, namely:

-   -   1. If <α> is True then apply Injunction β≈γ to φ, i.e. replacing         with γ any appearance of β in φ;     -   2. If <α> is False then do nothing to φ;     -   3. If <α> is Undefined then stop current transformation of φ,         which transmit Unknownness value.         A computer implemented method as in claim 22, further comprising         the step of: inserting LoF Algebraic Initials, Position &         Transposition, as Theorem type Definition in active Glossary;         initializing an active Glossary with hard-coded definitions of         string manipulations. The list of Hard-Coded Functions (HCF) may         be:     -   1. concatenation of a string on the right side into a string;         and updating the Current Substitution and the Rewriting Area;     -   2. de-concatenation of a string on the right side into a string,         and a character; and updating the Current Substitution and the         Rewriting Area;     -   3. concatenation of a string on the left side into a string; and         updating the Current Substitution and the Rewriting Area;     -   4. de-concatenation of a string on the left side into a string         and a character; and updating the Current Substitution and the         Rewriting Area;     -   5. generic equality of two formulas, including syntactic         equality of strings, by unifying, valuating—by using FCA, and         comparing syntactically their respective values, and updating         the Current Substitution and the Rewriting Area;     -   6. deactivation of a Well-Formed Syntactic Element, which turns         it into a mere and purely syntactical chain of symbols; and     -   7. quantification of a Formula by a variable, which develops         that quantified Formula by listing the variable on the Words         Table: “For All” Quantifier is developed as a generalized         conjunction; “There exists” Quantifier is developed as a         generalized disjunction.

The critical algorithm is selected from the group consisting of Formula Calculation Algorithm (FCA), Add Definition Algorithm (ADA) and Equation Resolution Algorithm (ERA).

A system for verifying, implementing and using a Semantic System of Intelligent Glossaries, the system comprising: an interpretation module having an initialization module, at least one critical algorithm, wherein the interpretation module provides a value for questions, which are set of formal texts containing at least one Well-Formed Syntactical Element; a Parsing module which processes texts of formal glossaries and formal questions; an Add Definition module for verifying a formal glossary, definition by definition, and for certifying compliance and consistency of the glossary; at least one active glossary for storing current glossaries of the whole system; a current substitution initialized with the empty set and updated after each translation; a Rewriting Area for computing on formulas, from the initial formal text of a question, up to its meaningful value; a Words Table, for storing natural language words and the name of their container glossary; a viewer module for editing glossaries and questions, and for interacting with actors; and a File update module for updating glossaries having at least one definition and associated interpretation from the interpretation module. The initialization module may provide system localization services, and data structures initialization. The parsing module may transform formal texts into lexical trees, containing Well-Formed Syntactic Elements and their properties; and automatically infer the type lexical element type of each Well-Formed Syntactic Element in the lexical trees. The translation module may: provide an interpretation for each lexical tree corresponding to a formal text; provide a graph of dependencies between nodes of the lexical trees during computation to detect cycles of computation; provide numbering of variable symbols to avoid collision between variables of a question and variables of a definition, or variables of deactivated sub-formulas of the same question; provide a cache pooling collection for memorizing previously computed formulas and their unique value, to optimize computation algorithms by retrieving values by rapid hash-coding access mechanisms. The at least one critical algorithm is selected from the group consisting of Hard-Coded Functions (HCF), Formulas Calculation Algorithm (FCA), Add Definition Algorithm (ADA), and Equation Resolution Algorithm (ERA). The system may have an Intelligent Glossary containing the ordered set of definitions for the lexical elements and at least one Minimal Lexicon generated from the Intelligent Glossary. The system may be implemented in the computer languages Microsoft .Net/Visual C#.

The computer-implemented method uses LoF Arithmetic for computing value of Forms; Forms are formal sentences resulting from questions containing only Literal symbols and chains of symbols, in accordance with the following conventions:

LoF Arithmetic Literal symbols and chains of symbols are:

-   -   1. Primary Symbols:         -   The symbol “[ ]”—Cross;         -   The symbol “⊥”—Space;         -   The symbol “@”—Arrobas;         -   Primary Symbols used singly are called Primary values;     -   2. Numbers (i.e. 0 1 2 . . . , 123, 30000, . . . ) expressed as         digits and chains of digits;     -   3. Words (i.e. “rule”, “customer”, “service”, . . . ) expressed         as chains of lower-case letters;     -   4. Arrows (i.e. 1         2, pending         invoiced, . . . ) expressed as Arrows of Primary Symbols, Words,         Numbers or other Arrows.

Convention of reference:

-   -   In LoF Arithmetic, the injunction “Take any form α” is a         contraction for:     -   1. Write a form;     -   2. Mark it with α;     -   3. Let α be its name;     -   4. Let the name indicate the form.

Convention of change:

-   -   1. In any form, a sub-form can be changed for an equivalent         form; such an equivalent change is called a step;     -   2. steps may be taken in either direction.

Hypothesis of simplification:

-   -   1. A normal form of a form is the simplest form into which, by         taking steps, it can be changed.     -   2. in accordance with LoF the result of that simplification—its         normal form—is unique.

Data Structures, operators, injunction and computation in LoF Arithmetic are formally defined as follows:

-   -   Elements, Bunches, Packages, and Arrangements are “The Forms”;         they are defined as follows;         -   1. Elements: Primary Values, Words, Numbers, and Arrows are             Elements; an Element is a Form;         -   2. Bunches: Bunches are inductively defined as follows: an             Element is a Bunch; If α and αβ are Forms, then the Calling             of α and β, i.e. αγ, is a Bunch; a Bunch is a Form;         -   3. Packages: Packages are defined as follows: If a is a Form             then the packaging of α, i.e. [α], is a Package; a Package             is a Form;         -   4. Arrangements: Arrangements are Forms that contain only             Primary Symbols.     -   LoF Operations:         -   1. Cross Operator:             -   Take any form aα; The Package [α] is the result of Cross                 Operator on α;         -   2. Space Operator:             -   Take any forms α and β; the Call αβ is the result of                 Space Operator on α and β;     -   LoF injunctions:         -   1. LoF injunction are formalized as Rewriting Rules on             Forms:             -   Take any forms α and β; “α≈β” stands for the Rewriting                 Rules:                 -   1. “Replace all occurrence of α with β into any                     forms where the sub-form α appears”.     -   The LoF Arithmetic injunctions are the following:         -   1. Omission of the symbol “⊥”:             -   [⊥]≈[ ];             -   ⊥⊥⊥≈⊥;             -   [ ]⊥⊥≈[ ]; ⊥⊥[ ]≈[ ];             -   @⊥⊥≈@; ⊥⊥@≈@;         -   2. The 2 axioms of George Spencer Brown:         -    Auto-Symmetry of Crossing:             -   Take any form α: [[α]]≈α;         -    Idempotence of Calling:             -   Take any form α: αα≈α;         -   3. Extension for Self-referential Element:         -    Dominance:             -   Take any form α: [ ]α≈[ ];         -    Abandonment of the Law of the excluded middle:             -   [@]≈@.         -   4. Extension for Bunches Rearrangement and Sorting:         -    Calling Commutativity:         -   Take any forms α and β: αβ≈βα; and         -    Calling Associativity:             -   Take any forms α, β and γ: (α β)γ≈α(βγ);     -   LoF Arithmetic is the rewriting of LoF Forms onto themselves, by         applying repeatedly LoF injunctions to reduce the number of         non-distinct sub-forms appearing in the initial form:         -   1. The normal form resulting is the value of the form;         -   2. Two forms are equal if, and only if, they have the same             value.

The computer-implemented method uses LoF Algebra for computing the value of Formulas; Formulas are formal sentences resulting from definitions and questions containing, in addition to Literal Symbols, non-Literal Symbols, Identifiers and variables, with the following conventions.

-   -   The main non-Literal Symbols are:         -   1. The Symbols of Definition, in accordance with the present             computer implemented method, namely: “|−” “≈” “;”         -   2. The Linguistic symbols, which are used to formalize             semantic relations between Natural Language words (i.e. the             “is” symbol “.”, the “is a” symbol “:”, the subsumption             symbol “             ” . . . );         -   3. The Logical symbols (i.e: quantifiers (∀, ∃), logical             connectors, i.e “             ”, “             ”, “             ”, “             ”, . . . );         -   4. The Mathematical symbols (i.e. arithmetical symbols             (“+”,“−,“/””, “×”), equality symbol (“=”), function symbol             (“→”), function application symbol (“_”), . . . ).     -   An Identifier is a codification or a label beginning with an         Uppercase Letter; for example: “Zip code”, “Postal code”,         “CUSTOMER” Data Base, “Posting” process . . . ; An Identifier is         not a word;     -   Identifiers, non-Literal Symbols and Words are the Lexical         Elements;     -   An Arity, a Sort of Value, and a Notation are assigned to each         Syntactic Element:         -   1. Arity is a whole number:             -   Words, Numbers and Identifiers are 0-Arity Lexical                 Elements;             -   Symbols are either 1-Arity (unary), or 2-Arity (binary).         -   2. The authorized Notations for Symbols are:             -   Infix notation: the binary symbol is inserted between                 its (two) arguments;             -   Prefix notation: the unary symbol is attached to the                 beginning of its arguments;             -   Suffix notation: the unary symbol is attached at the end                 of its arguments;             -   Circumfix notation: the unary symbol is placed around                 its unique argument (bracketing).         -   3. The Sorts of Value of non-Literal Lexical Elements are             given in accordance with their usage, i.e.:             -   Logical symbols have Fixed Truth-values;             -   Semantic Relation symbols have Fixed Truth-values;             -   Arithmetical symbols (i.e. Addition or Multiplication                 symbols) have Fixed Numerical Reality-values;             -   Mathematical function symbols may have Changing values,                 either Reality (i.e. n→n+1) or Truth (i.e.: A→                 A) values;             -   Identifiers built out of uppercase letters only are                 predicate: they have Changing Truth-values;             -   Identifiers built out of at least one uppercase                 letter—the first letter—followed by at least another                 letter: are mathematical functions: they have Changing                 Reality-values (Numerical or Non Numerical);     -   A Variable is a symbol which can be substituted with any         arbitrary formula:     -   1. The Variable symbols are standalone upper-case letters, i.e.         A, B, C . . . X, Y, Z;     -   2. Variable symbols are 0-Arity Syntactic Elements;     -   Symbols, Words, Numbers, Identifiers, Arrows, and Variables are         called Syntactic Elements;     -   The formal text of a formula consists of combining Syntactic         Elements, either Literal or non-Literal, while respecting their         sort, arity and notation.     -   A Ground Formula is a Formula with no free variables; A         Non-Ground Formula is a Formula with at least one free variable:     -   A Primary Formula is a Non-Ground Formula containing only         Primary Symbols and Variables:         -   1. A Primary Expression is a Primary Formula, which is an             Expression;         -   2. A Primary Term is a Primary Formula, which is a Term;     -   A Clause is a Primary Formula of the form “[[X][Y]]” or “[X[Y]]”         or “[[X]Y]”;     -   A Disjunctive Primary Formula is a Primary Formula built by         Calling 2 or more Clauses, i.e. of the form “[[A][B]] . . .         [[Y][Z]]”.

A Formula is either an Expression or a Term, depending on the sort of Value of the Lexical Elements it contains:

-   -   An Expression has a Truth-value; a Term has a Reality-value;     -   An Indication is a Formula made up of a unique Symbol         concatenated with variables or other 0-arity Elements,         respecting the sort, arity and notation of that unique Symbol:         -   1. An Indication is an atomic Formula for LoF Calculus of             Indications.         -   2. A Indication Expression is an Indication, which is an             Expression;         -   3. A Indication Term is an Indication, which is a Term;     -   An Ordinary Formula is a Formula made up of a unique Symbol         concatenated with other Ordinary Formulas, respecting the sort,         arity and notation of the unique Symbol:         -   1. An Ordinary Formula is a non-atomic Formula, for LoF             Calculus of Indications;         -   2. A Ordinary Expression is an Ordinary Formula, which is an             Expression;         -   3. An Ordinary Term is an Ordinary Formula, which is a Term;     -   A Primary Indicative Formula is a Formula containing only         Literals, Primary Symbols, Variables, and Indications:         -   1. A Primary Indicative Expression is a Primary Indicative             Formula, which is an Expression;         -   2. A Primary Indicative Term is a Primary Indicative             Formula, which is a Term;

Variables are used for Unification, Assignment, and Substitution, as follows:

-   -   The Unification process consists of binding unified variables         with their respective sub-formulas in a Source Formula;     -   Elements are constants: they are only unifiable with themselves;     -   Variables can be unified with other Formulas, for example:         -   1. Source Formula −2 is unifiable with −V:             -   V is assigned the sub-formula 2, which is notated by the                 binding “V\2”;         -   2. Source Formula −(2+4) is unifiable with −V:             -   V is assigned the sub-formula (2+4), which is notated by                 the binding “V\(2+4)”;         -   3. Source Formula (−2+4) is not unifiable with −V;         -   4. Source Formula (4+4) is unifiable with (V+V):             -   V is assigned the sub-formula 4, which is notated by the                 binding “V\4”;         -   5. Source Formula (2+4) is not unifiable with (V+V);         -   6. Both Source Formulas (2+4) and (2+2), are unifiable with             (V+W);     -   The Substitution process consists of changing unified variables         by their respective formulas, into any target formula:         -   1. If the same variable occurs more than once in a formula             then we must substitute with the same sub-formula at each             occurrence of this variable in the target formula;         -   2. Different variables can be substituted with the same or             different sub-formulas.     -   Placing Symbols between Syntactic Elements makes some Formulas         ambiguous; for example: Formula “1+2*3” might mean: 1 and 2 are         added, and then the result is multiplied by 3 giving 9 or 1 is         added to the result of multiplying 2 by 3, giving 7; Parentheses         symbols can be used to disambiguate formula's unification, by         indicating the order of evaluation; for example: 1+(2*3) or         (1+2)*3;     -   Single quotation marks are used to deactivate Non-Ground         Formulas; Deactivated Formulas are considered as Ground         Formulas, by considering all their Variables as Elements (or         “Pseudo-constants”);     -   Double quotation marks are used to designate a formula as a         chain of symbols;     -   An Assignment of Variables is a set of bindings given on these         Variables, in accordance with the Unification process.

By extension, LoF Algebra encompasses LoF Arithmetic, as follows:

-   -   LoF Forms, either Elements, Bunches, Packages or Arrangements,         have equivalent Algebraic Formulas, named Literals:         -   1. A Literal represents literally a Form of LoF Arithmetic             in LoF Algebra;         -   2. A Literal is a Ground formula: it cannot be substituted;         -   3. A Literal Expression is a Literal, which is an             Expression;         -   4. A Literal Term is a Literal, which is a Term;     -   The Sort of Value of Literals in LoF Algebra are:         -   1. Numbers have Numerical Reality Fixed values.         -   2. Words have Non-numerical Reality Fixed values;         -   3. Arrangements have Truth Fixed values;         -   4. Arrows have Changing-values, either Truth or Reality;         -   5. Primary symbols are polymorphic, i.e.:             -   Primary symbols singly have Truth values (either Fixed                 or Changing);             -   Primary symbols used with Numbers, Words and Arrows have                 Reality values (either Fixed or Changing).     -   To Cross is considered as an unary operation whose symbol is a         Cross with a circumfix notation;     -   To Call is considered as a binary operation whose symbol is a         Space with an infix notation     -   A Primary Expression is said to be satisfiable if there is some         assignment of Variables that will turn it into a Literal         Expression, evaluated to [ ] (Cross) by LoF Arithmetic;         otherwise, it is said to be unsatisfiable:         -   1. A Clause Expression of the form “[[X]X]” or “[X[X]]”, for             some variable X, is not satisfiable.         -   2. A Disjunctive Expression is satisfiable if, and only if,             one of the Clauses it contains is satisfiable; this can be             checked in polynomial time.

In the computer-implemented method, processing a formula consists of Algebraic Mechanisms of Substitution, Replacement, Pre-condition and Normalization, as follows:

1. Replacement:

-   -   If (α≈β), and if δ is a formula constructed by replacing by β         any appearance of α in γ, then (γ≈δ);

2. Substitution:

-   -   If (α≈β), and if every instance of a given independent variable         υ in (α≈β) is substituted with a formula ω, without being         necessary for υ and ω to be equivalent or for ω to be constant         or variable, and if as a result of this procedure α becomes γ         and β becomes δ, then (γ≈δ);

3. Pre-condition:

-   -   A preliminary condition—a pre-condition—is a constraint that an         injunction must satisfy in order to be acceptable in rewriting:         -   i. A pre-condition delimits the acceptability of             transformation from source to target by an injunction;         -   ii. Pre-conditions are Expressions (i.e. Truth-valued             Formulas);         -   iii. “α|−η” stands for the execution of injunction η,             constrained by the satisfaction of formula α.

4. Normalization:

-   -   Normalizing a Primary Expression is turning it into a         Disjunctive Expression, while eliminating all non-satisfiable         Clauses it contains;         -   i. Normalization a Primary Expression preserves the semantic             of that Primary Expression.     -   Normalizing a Primary Expression consists of repeatedly applying         the LoF Algebraic Initials:         -   i. Position: [[X]X]≈⊥;         -   ii. Transposition: [[XY] [XZ]]≈X[[Y][Z]]; [[YX]             [ZX]]≈[[Y][Z]]X;

In the computer-implemented method, the following instructional sentences are defined in accordance with the Algebraic Mechanisms:

-   -   “Apply Injunction β≈γ to Formula φ” means rewriting formula φ,         through the Algebraic Mechanisms of Unification and Assignment,         Substitution and Replacement.     -   “Apply Definition α|−β≈γ in Glossary κ to Formula φ” is defined         by the combination of Applying Injunction and Pre-condition,         namely:         -   1. If <α>=[ ] then FCA (Apply Injunction β≈γ to formula φ)         -   2. If <α>=⊥ then do nothing to φ         -   3. If <α>=@ then stop current transformation of φ, and             return @, which transmit unknowingness;     -   “Apply Glossary κ to Formula φ” is recursively defined by:         -   1. For all applicable definitions α|−β≈γ in the glossary κ,             -   Apply Definition α|−β≈γ to Formula φ;             -   The result is the value of the formula, which is notated                 <φ>; “Apply Glossary κ to Formula φ with Mode μ” is the                 core function of Formula Calculation Algorithm (FCA).     -   “Draw consequences of Assertion and Theorem ([ ]-β≈γ) using         glossary κ”, is defined by:         -   1. γ is either [ ] (Cross) for Assertion or Theorem, or ⊥             (Space) for Negative Assertion or Antitheorem;         -   2. Apply Glossary η to Formula β giving <β>, which is a             Primary Indicative Formula in which Unknown Indications             represent primary values;         -   3. Change <β> into a Primary Formula by replacing all             Unknown Indications, by primary Variables;         -   4. Compute Set of solutions of equation: <β>≈γ; For all             coherent set of primary solutions:             -   {σ₀, σ₁, σ₂, . . . }, whose primary value are                 respectively:                 -   {υ₀, υ₁, υ₂, . . . }:             -   insert into glossary κ the set of definitions:                 -   {[ ]|−σ₀≈υ₀, [ ]|−σ₁≈υ₁, . . . }     -    “Draw consequences of Assertion and Theorem ([ ]|−β≈γ) using         Glossary κ”, is the core function of Equation Resolution         Algorithm (ERA).     -   “Normalize Terminology or Theorem α|−β≈γ using Glossary κ” is         defined by:         -   1. Inserting LoF Algebraic Initials, Position &             Transposition, as Theorems in Glossary κ;         -   2. If Definition α|−β≈γ is a Terminology, then:             -   Apply Glossary κ′ to Formula α for Normalizing;                 Expression α is changed to Primary Expression α′;             -   Change temporarily all free variables of Formulas α′ and                 γ into pseudo constants;             -   Draw consequences of Assertion or Theorem ([ ]|−α′≈[ ])                 using Glossary κ); Change temporarily Glossary κ to κ′;             -   Apply Glossary κ′ to Formula γ for Normalizing; Formula                 γ is changed to Primary Formula γ′;             -   Insert into glossary κ the definition α′|−β≈γ′;         -   3. If Definition α|−β≈γ is a Theorem, then:             -   γ is either [ ] (Cross) for a Theorem, or ⊥ (Space) for                 an Antitheorem;             -   Apply Glossary κ to Formula β for Normalizing; Formula β                 is changed to β′;             -   Insert into glossary κ the definition α|−β′≈γ;         -   4. If Definition α|−β≈γ is a Question without Pre-condition,             then:             -   Apply Glossary κ to Formula β for Normalizing; Formula β                 is changed to β′;             -   Insert into glossary κ the definition α|−β′≈γ;         -   5. If Definition α|−β≈γ is a Question with Pre-condition,             then:             -   Change temporarily all free variables of Expression α                 into pseudo constants; Expression α is changed to                 Primary Expression α′;             -   Draw consequences of Assertion or Theorem ([ ]|−α′≈[ ])                 using Glossary κ); Change temporarily Glossary κ to κ′;             -   Apply Glossary κ′ to Formula β for Normalizing; Formula                 β is changed to Primary Formula β′;             -   Insert into glossary κ the definition α′|−β′≈γ;     -    “Normalize Definition α|−β≈γ using Glossary κ” is the core         function of Add Definition Algorithm (ADA).

The computer-implemented method uses injunctions as conditional instructions to transform a formula for eliminating the number of non-Literal symbols, without changing its value; by the Algebraic Mechanisms, the variables are assigned in the Current Substitution with the corresponding syntactic elements in the formula; the result is a Form which can be processed by the LoF Arithmetic to compute its unique value. LoF Algebra brings a mechanism for normalizing any Formulas into Primary Formulas for comparing semantically such Primary Formulas, and therefore any Formulas.

The interpretation process starts by translating “on the spot” the question's ground formal text, by applying a definition for each lexical element contained in the question, in accordance with the Algebraic Calculation. At the lowest level, only words, numbers and primary symbols appear: it is a literal formula. The interpretation process stops by sorting, rearranging and reducing the literal formula to its value, in accordance with the LoF Arithmetic.

FIG. 1 depicts the synopsis of the computer implemented method used to create, verify, interpret, use and update a Semantic System of Intelligent Glossaries (SSIG) 5.

Knowledge Manager (12) codes formal definition sentences having the same semantics as original natural language definition sentences. A formal glossary (14) contains the ordered set of definitions covering the key words usable to express essential knowledge (10) necessary and sufficient for the activity in a given field of endeavor. Each definition in a formal glossary (14) may be selected from the group consisting of terminology, assertions, theorems and questions & answers. A formal glossary (14) may also refer to other formal glossaries.

A formal glossary is consistent with LoF, if it respects all field specific distinctions: each lexical element results in a Distinction-Based reasoning by the Knowledge Manager (12); field specific distinctions are formalized as indications and formally defined in the formal glossary (14). Formal specifications of the present computer implemented method can be written as a formal glossary (12), which may be named the Self-Referential Glossary; the compliance of any formal glossary with the present computer implemented method is checked by processing it as the ground formal text of a question, through quotation marks, by using the Self-Referential Glossary within a SSIG (16). A formal glossary, which is certified to be consistent within such a SSIG, becomes an initial Intelligent Glossary in that SSIG 5. A Minimal Lexicon (18) is a lexicon automatically generated from an Intelligent Glossary (20), which leads to a consistent lexicon of semantically independent lexical elements.

Questions are ground formal sentences having the same semantics as original natural language questions sentences; Formal questions (22) with free variables are turned into ground sentences by pre-conditioning all the variables they contain. The Interpretation System transforms questions into their responses; both knowledge actors and automated knowledge information system (24) can query formal questions (22) to the Interpretation System. The Intelligent Glossary (20) evolves through use, by saving a question (22) and its answer (23) as a new question & answer definition.

FIG. 2 depicts the internal of an Interpretation System (50) for implementing a SSIG 5, including an Interpretation module (52), which uses at least one critical algorithm (e.g. 54, 56, 58). The Current Substitution is a set of bindings (variable, formula) containing assignments of variables; the Current Substitution is initialized with the empty set and updated after each interpretation. The texts of formal glossaries (60) and formal questions (62) are parsed using the parsing module (63), structured by types of syntactic elements and stored into lexical trees by the Parsing Module (63); If no parsing errors are found, then the glossary (64) is checked for semantically duplicate definitions and for consistency, by applying the self-referential glossary imbedded within the SSIG, by the Check and Certification module; natural language words, together with the name of their container glossary, are stored into the Words Table (65); if all glossaries of the SSIG are correct, the corresponding Active Glossary (64) is initialized by the module; It is envisioned that a number of different algorithms may be used. By way of example, though, the algorithm may be the Add Definition Algorithm (ADA) (66), the Formula Calculation Algorithm (FCA) (56) or the Equation Resolution Algorithm (ERA) (54). The algorithms may be updated by the files update module (76), which is in communication with the intelligent glossaries (20) and lexicons (18). The Interpretation module (52) provides an interpretation for a set of formal texts containing at least one lexical element. The text from the question may be rewritten in the rewriting area (68) or substituted in the current substitution (70), delivered to the viewer module (72) and provided as an answer (74)

FIG. 3 depicts the data model and the process model of the computer-implemented method of determining the meaning of formal written language constructs in accordance with the present invention.

FIG. 4 depicts a large Knowledge Management System for verifying, implementing, sharing and using a common Semantic System of Intelligent Glossaries and their related Minimal Lexicons, organizing a decentralized network of Internet documents and highly parallel computer applications using well-defined interfaces, i.e. in XML language; this provides the capability to export data definitions for describing formal interfaces; and to query online properties of lexical elements, inferable from their definition and theorems.

All natural language words, symbols and identifiers acquire the same meaning for the whole system (single meaning); this provides the capability to operate semantically, i.e. preserving the single meaning of words, on such lexicons—considered as sets of lexical elements—with the usual set operators (union, intersection, complement, set difference, symmetric difference) in order to construct complex lexicons, as combinations of lexicons (minimal or complex); such a complex lexicon is a thesaurus, covering specifically a business or a field of endeavour, for searching, selecting and clustering with regard to a group of keywords, belonging together to a complex lexicon; this is called an Intelligent Retrieval. An Intelligent Retrieval on Web documents, written by authors who respect the single meaning defined in the glossaries of the SSIG, enables computers to compute precisely the probability that the document in question is about—or not—a specific business or field of endeavour; for example:

-   -   If 80% of terms contained in the lexicon of logics, and 90% of         terms contained in the lexicon of arithmetic, occur in a text         written by an author who respects the single meaning of words         and symbols defined in Intelligent Glossaries then,     -   There is almost 100% probability that this text is about         arithmetic & logics;         The main differences with statistical approaches, based on the         usage and frequency of words occurring in free texts, are:     -   1. The keywords—or their formal synonyms—are the high-frequency         words appearing within written texts in that field of endeavor;     -   2. These keywords are well defined lexical elements, and         purposely occur in the texts with their single meaning;     -   3. The lexicons—considered as sets of keywords—are automatically         generated from the certified glossaries containing the single         meaning definition of keywords;         An Intelligent Retrieval can be launched in parallel distributed         processing, on all the formal glossaries of an SSIG; and on a         corpus of documents on the Internet. Computer aided translations         into another natural language can also be automated by using a         SSIG. Lexical Element can be made language independent, by         coding them as chains of symbols:     -   This allows to automate translation of definitions to build a         multilingual SSIG;     -   The Single meaning of words allows a one-to-one translation in         multilingual lexicons;     -   Usage of language dependent synonyms permits richer         translations;

FIG. 5 depicts the textual and graphical notations used in the description of the main algorithms in FIGS. 6 & 7.

The basic manipulations, not definable in the computer implemented method, consist of Hard-Coded Functions (HCF) and equations for the manipulation of strings of symbols, such as:

-   -   concatenation of a string on the right side into a string; and         updating the Current Substitution and the Rewriting Area;     -   de-concatenation of a string on the right side into a string,         and a character; and updating the Current Substitution and the         Rewriting Area;     -   concatenation of a string on the left side into a string; and         updating the Current Substitution and the Rewriting Area;     -   de-concatenation of a string on the left side into a string and         a character; and updating the Current Substitution and the         Rewriting Area;     -   generic equality of two formulas, including syntactic equality         of strings, by unifying, valuating—by using FCA, and comparing         syntactically their respective values, and updating the Current         Substitution and the Rewriting Area; and     -   deactivation of a Well-Formed Syntactic Element, which turns it         into a mere and purely syntactical chain of symbols.     -   Quantification of a Formula by a variable, which develops that         quantified Formula by listing the variable on the Words Table:         -   1. A “For All” Quantifier (universal quantifier, typically             ∀), is developed as a generalized conjunction on all words             in the Words Table;         -   2. A “There exists” Quantifier” (existential quantifier,             typically ∃), is developed as a generalized disjunction on             all words in the Words Table;

FIG. 6 depicts one embodiment of an implementation utilizing The Formulas Calculation Algorithm (FCA). FCA carries out a backtracking inference. Its purpose is to rewrite a formula by replacing sub-formulas in accordance with all their applicable definitions, up to a literal formula is obtained: each time that a lexical element appears, it is translated by the formula of its definition, which reduces the number of non-primary symbols in the formula through the calculation process; the meaning of a formula, in accordance with a terminology definition, is the simpler formula obtained by applying that definition to the initial formula; the sequence of two definitions of the same glossary is the composition of their respective meaning; the FCA operates on the entire glossary, which enables it to evaluate language constructs built on previously defined lexical elements.

FCA is used for applying glossaries to a formula, with different modes (either all undefined indications are changed to @ or all undefined indications remains “as is”); there are two possible cases to which this is applied:

-   -   Case 1. For a formula that is an expression, corresponding to a         declarative sentence (a statement);     -   Case 2. For a formula that is a term, corresponding to a naming         sentence (for naming an object or a state).

In Case 1, the response of a glossary to a expression is the primary value obtained by applying the tree of all applicable definitions from glossaries of SSIG, to the sub-expressions of the expression; depending on the mode, FCA keeps the unresolved indications as is, instead of valuating them by @; this leads to a primary expression, containing only indications and primary symbols; otherwise the process stops when nothing but primary symbols remain: this is an arrangement. After being reduced by LoF, this arrangement becomes a primary value which is interpreted semantically as follows:

-   -   a. “[ ]” means that the expression is true;     -   b. “ ” (or “⊥”) means that the expression is false;     -   c. “@” means that the expression is undefined, as there remains         at least one unsolved indication.         The proof of the value of an expression in accordance with the         glossary applied is the arrangement calculated by applying the         glossary to this expression; by the value obtained through its         reduction, the arrangement proves the value of the expression.

In Case 2, the meaning of a term in accordance with a glossary is the bunch obtained by applying the sequence of definitions from glossaries of SSIG, to the sub-terms of the term. The algorithm stops when nothing but a collection of words, numbers, and primary symbols remain, which can be semantically interpreted by themselves.

For reuniting the 2 Cases, 1 & 2, the Knowledge Manager (12) may write an equation in the form of @=Y to express a term being defined Y, as an expression; when processing that expression, the hard-coded generic equality recognizes the Unknown Element, @ and interprets it “on the spot” as referring the current sub-term in the question where it appears; that current sub-term is then replaced by the value of Y; this can be reused for a complex term, which is thereafter simplified as a result.

FCA can be used for normalizing the formulas of any definition; in that case: undefined, recursive, hard-coded, and quantified indications are not changed; terminologies in which the indicative part contains at least one constant are not applied; and preconditions are deactivated by the quote function before evaluation.

FIG. 6 depicts another embodiment of an implementation utilizing the Add Definition Algorithm (ADA) and the Equation Resolution Algorithm (ERA). Upon loading the glossary, each definition is checked, normalized and inserted by applying ADA. The comprehension of an assertion is the set of logical consequences (called the derived assertions) that can be drawn from its insertion into the glossary. ERA implements a “forward tracking” inference for simulating that comprehension mechanism: each assertion is interpreted as an equation, where the left-hand term of that equation is a primary expression obtained by applying FCA to the indicative part of the assertion without changing unknown assertions, and the right-hand term of that equation is the primary value of the assertion. That equation is solved through enumeration and a derived assertion is inserted for each indication contained in the primary expression, and its primary value solution. ERA stops when it obtains an expression defined by @. ERA intervenes for respecting theorems, by applying FCA to the indicative part of the theorem, which is a non-ground formula; this leads to creating new derived assertions, by substituting variables with coherent values from compatible assertions contained in the glossary. ERA intervenes also when encountering questions with variables and a pre-condition: it solves the equation by equating the pre-condition to [ ]; ERA keeps the tree of coherent solutions of the pre-condition equation; for each branch of the tree of solutions, ERA inserts a derived assertion for evaluating the corresponding variables temporarily in order to compute the question itself. If the expression contains a quantifier on a word, ERA develops it on the Words Table, which is the set of all applicable Natural Language Words, for computing direct solutions.

It should be understood that the foregoing relates to preferred embodiments of the invention and that modifications may be made without departing from the spirit and scope of the invention as set forth in the following claims. 

1. A computer implemented method of determining the meaning of formal language constructs occurring in written texts, said method comprising the steps of: providing an alphabet and a set of symbols for constructing lexical elements, and syntactic elements built on said alphabet, lexical elements, and symbols on at least one computer; determining, by said at least one computer, a sort of value, an arity, a notation, and a type for each said syntactic element, to provide well-formed syntactic elements and meaningless syntactic elements; building, by said at least one computer, formal definitions from said well-formed syntactic elements, and determining a type for each said formal definition to provide a list of terminologies, assertions, theorems, questions and answers; building, by said at least one computer, at least one formal glossary as ordered sets of said formal definitions; providing, on said at least one computer, to an actor at least one said formal glossary, and a related minimal lexicon; parsing, verifying and normalizing each said formal definition, by said at least one computer, from said formal glossary, to provide a list of defined lexical elements and undefined lexical elements; allowing said actor to refer, search, cluster or select written texts, on said at least one computer, from said defined lexical elements contained within minimal lexicons and appearing within said written texts; acquiring questions from said actor, on said at least one computer, wherein each said question is a set of formal texts containing at least one well formed syntactic element; parsing, verifying and normalizing each said well formed syntactic element in said questions, by said at least one computer; retrieving, by said at least one computer, for each said defined lexical element contained within said questions, all the applicable formal definitions from said formal glossary; applying, by said at least one computer, said formal definitions to said defined lexical elements in said questions in accordance with an interpretation process having at least one critical algorithm; providing at least one values to said actor on said at least one computer; coding each said question and a meaningful value as a new questions and answers definition; and saving said new questions and answers definitions in said formal glossary, which turns said formal glossary into a new intelligent glossary.
 2. A computer implemented method as in claim 1, further comprising the steps of: selecting an alphabet containing at least Lowercase Letters, uppercase Letters, and digits to provide a set of symbols on said at least one computer; selecting from said set of symbols, three primary symbols on said at least one computer; assigning the term primary value to any primary symbol used singly; assigning the term ordinary symbols to any other symbol from said set of symbols; assigning the term word to any chain of lowercase letters, coding natural languages words; assigning the term number to a chain of digits, coding natural whole numbers; assigning the term elements to the group consisting of primary values, words, numbers, and arrows; assigning the term arrow to any element separated from either an element or an arrow by a change symbol; assigning the term identifier to a chain of letters or digits beginning by an uppercase letter; assigning the term lexical elements the group consisting of words, identifiers, and ordinary symbols; selecting variable symbols in the group consisting of uppercase letters used singly; and assigning the term syntactic elements to the group consisting of symbols, words, numbers, identifiers, arrows, and variables.
 3. A computer implemented method as in claim 1, further comprising the step of assigning a data attribute notation to each syntactic element that is a symbol, wherein each said symbol has a symbol argument, said step of assigning a data attribute comprising the steps of: assigning a prefix notation for a symbol that is attached to the beginning of said symbols arguments; assigning a postfix notation for a symbol that is attached at the end of said symbols arguments; assigning a infix notation for a symbol that is inserted between said symbols arguments; assigning a circumfix notation for a unary symbol that is placed around said symbols arguments.
 4. A computer implemented method as in claim 1, further comprising the steps of: selecting sorts of value in the group consisting of truth-values and reality-values, sub-sorted into numerical, non numerical reality; determining, by said at least one computer, if said sort of value is either a fixed value or changing value; assigning, by said at least one computer, a unique sort of value to each ordinary symbol; processing, by said at least one computer, Primary symbols as syntactic elements with polymorphic sorts.
 5. A computer implemented method as in claim 1, further comprising the steps of: assigning an arity equal to zero to elements, variables, and identifiers; assigning to each ordinary symbol, an arity equal to the number of authorized arguments; computing, by said at least one computer, the arity of primary symbols intangled inside or around other syntactic elements, in accordance with their position in regards to said syntactic elements.
 6. A computer implemented method as in claim 1, further comprising the steps of: assembling a unique symbol concatenated with only 0-arity syntactic elements, respecting the sort of value, arity and notation of said unique symbol to provide a well formed syntactic element; calling such a well formed syntactic element atomic; assembling a unique symbol concatenated with other said well-formed syntactic elements, atomic or non-atomic, respecting the sort, arity and notation of said unique symbol, and using parentheses to disambiguate the order of evaluation of syntactic elements; such a well-formed syntactic element is called non-atomic; calling all other forms of syntactic elements ill-formed; calling “the head”, the unique symbol of said well formed syntactic element, atomic or non-atomic; calling “the body”, the rest of said well formed syntactic element; calling “the sort of value of a well formed syntactic element” the sort of value of the head of that well formed syntactic element; calling “bound” an occurrence of a variable which is in said body of a quantifier or a function symbol in a well formed syntactic element; calling “free” an occurrence of a variable which in not in said body of a quantifier or not a function symbol in a well formed syntactic element; calling “ground” a well formed syntactic element which contains no free variables; calling “non-ground” any well formed syntactic element which is not “ground”; calling “literal”, a well formed syntactic element which contains only elements, and primary symbols; calling “non-literal” any well formed syntactic element which is not “literal”.
 7. A computer implemented method as in claim 1, wherein said well-formed syntactic elements are typed in said at least one computer as: instructions, wherein said instructions contain at least one symbol of definition and said Instructions are sub-typed as: injunctions, built on two formulas, said two formulas comprising: the indicative part and the body surrounding the infix symbol of definition.
 8. A computer implemented method as in claim 1, wherein each formal definition has a definition type selected from the group consisting of terminology, assertions, theorems and questions and answers.
 9. A computer implemented method as in claim 1 wherein, a defined lexical element is the unique lexical element that appears within a atomic indicative part of a three-part pattern coded terminology definition.
 10. A computer implemented method as in claim 1, further comprising the steps of: providing to said actor at least one intelligent glossary on said at least one computer; parsing and verifying, by said at least one computer, said formal glossaries and their formal definitions to provide the type of syntactic elements they contain; ordering and storing said formal definitions from said formal glossaries in said at least one computer.
 11. A computer implemented method as in claim 10, further comprising the step of: producing, by said at least one computer, a minimal lexicon build from defined lexical elements that appear in a indicative part of a definition in said formal glossary.
 12. A computer implemented method as in claim 1, wherein said step of allowing an actor to cluster or select written texts from lexical elements contained within minimal lexicons and appearing within said written texts, is further comprised of the steps of: respecting field specific distinctions, as each lexical element contained within a minimal lexicon is the indication in a distinction, in accordance with laws of form calculus of distinctions; modularizing, by said at least one computer, a field of endeavor into domains by using distinctions applicable to one domain, for drawing precise boundaries with all other domains in that field of endeavor; providing, by said at least one computer, a single meaning to all natural language words, symbols and identifiers for the whole system of minimal lexicons, considered as sets of lexical elements, from intelligent glossaries; preserving the single meaning of elements of said minimal lexicon with a usual set operators in order to construct complex Lexicons for a specific field of endeavour; selecting key-words from written texts on said at least one computer, wherein said key-words are the high-frequency words appearing within said written texts in said specific field of endeavor; semantic researching on the internet or intranet by identifying said key-words key-words with lexical elements contained in minimal lexicons generated from intelligent glossaries of said domains.
 13. A computer implemented method as in claim 1, further comprising the steps of: accepting from said actor, by said at least one computer, a question which is a set of formal texts containing at least one well-formed syntactic element, wherein the value of said well-formed syntactic element is unknown; parsing and verifying, by said at least one computer, the formal text of said question to infer the type of syntactic element it contains, and to produce formulas contained in the question; and initializing the rewriting area with the formulas contained in the question, by said at least one computer.
 14. A computer implemented method as in claim 13, further comprising the steps of: retrieving for each said formula in a rewriting area, all matching formal definitions from formal glossaries, using algebraic mechanisms of unification and instantiation; eliminating redundant or inconsistent matching definitions, by said at least one computer, to provide an optimized tree of applicable definitions, and its related current substitution; building the tree of all applicable definitions from formal glossaries, to each sub-formula of the formulas in the rewriting area.
 15. A computer implemented method as in claim 13, wherein said interpretation process is further comprising the steps of: starting by translating, by said at least one computer, each sub-formula of said formulas in a rewriting area, in accordance with the algebraic mechanisms of substitution and replacement, and continues up to a literal formula appears; stopping by reducing said literal formula in said rewriting area of said at least one computer, in accordance with the laws of form calculus of indications for computing its normal form, which is its value; by laws of form, said value is unique.
 16. A computer implemented method as in claim 15, wherein said step of translating a each sub-formula is further comprising the steps of: applying, by said at least one computer, formal definitions from the tree of all applicable definitions, to sub-formulas of said formula in said rewriting area; considering formal definitions as conditional rewriting rules, to transform said formula while preserving its value; combining and comparing different results from a tree of all applicable definitions, to produce a unique meaningful value; and coding said unique value of said formula, by said at least one computer.
 17. A computer implemented method as in claim 16, wherein applying _formal definitions is precisely defined by the combination of a pre-condition and injunction mechanisms, comprising: if a predetermined criteria is true then apply Injunction; if a predetermined criteria is _false then do nothing; if a predetermined criteria is undefined then stop current transformation and transmit an unknownness value.
 18. A computer implemented method as in claim 1, further comprising the step of: inserting algebraic Initials, position & and transposition, as theorem type definition in active glossary, in said at least one computer; initializing an active glossary, in said at least one computer, with hard-coded definitions of string manipulations.
 19. A computer implemented method as in claim 18, further comprising a list of hard-coded functions, wherein the list of hard-coded functions comprises: concatenation of a string on the right side into a string; and updating the current substitution and the rewriting area; de-concatenation of a string on the right side into a string, and a character; and updating the current substitution and the rewriting area; concatenation of a string on the left side into a string; and updating the current substitution and the rewriting area; de-concatenation of a string on the left side into a string and a character; and updating the current substitution and the rewriting area; generic equality of two formulas, including syntactic equality of strings, by unifying, valuating—by using FCA, and comparing syntactically their respective values, and updating the current substitution and the rewriting area; deactivation of a well-formed syntactic element, which turns it into a mere and purely syntactical chain of symbols; and quantification of a formula by a variable, which develops that quantified formula by listing said variable on a words table: “for all” quantifier is developed as a generalized conjunction; “there exists” quantifier is developed as a generalized disjunction.
 20. A computer implemented method as in claim 1, wherein said critical algorithm are the formula calculation algorithm (FCA), the add definition algorithm (ADA); and the equation resolution algorithm (ERA).
 21. A computer implemented method as in claim 1, further comprised of the step of: providing an answer, by said at least one computer, to said actor as the meaningful value of a syntactic element, if said syntactic element is not meaningless; coding said meaningful value of a well formed syntactic element as a question and answer type definition; and saving in said at least one computer said formal glossary of said result definition, in accordance with said types of definition.
 22. A computer implemented method of determining the meaning of formal language constructs occurring in written texts, said method comprising the steps of: providing on said at least one computer an alphabet and a set of symbols for constructing lexical elements, and syntactic elements built on said alphabet, lexical elements, and symbols; determining by said at least one computer a sort of value, an arity, a notation, and a type for each said syntactic element, to provide well-formed syntactic elements and meaningless syntactic elements; building formal definitions from said typed wellformed syntactic elements, and determining a type for each definition to provide a list of terminologies, assertions, theorems, questions and answers; and building formal glossaries as ordered sets of formal definitions; acquiring from a knowledge manager a formal glossary content; parsing, verifying and normalizing each formal definition contained in said formal glossary, to provide a list of defined lexical elements and undefined lexical elements; drawing consequences of each assertion and theorem of the formal glossary, to compute new derived assertions and to check compliance with existing terminologies, in accordance with an interpretation process having at least one critical algorithm; acquiring questions from an actor, wherein each said question is a set of formal texts containing at least one well formed syntactic element; parsing, verifying and normalizing each well formed syntactic element in the question; retrieving, for each defined lexical element contained within said questions, all the applicable formal definitions from said formal glossary; applying said formal definitions to said defined lexical elements in said questions in accordance with an interpretation process having at least one critical algorithm; providing at least one values to said actor; coding each said question and its meaningful value as a new question and answer definition; processing a formal glossary as a set of formal texts, using a self-reference to certify said formal glossary; and saving said certified formal glossary and its related minimal lexicon in said at least one computer, wherein said lexicon is comprised of at least one well defined lexical element, as an initial intelligent glossary.
 23. A computer implemented method as in claim 22, further comprising the step of constructing lexical and syntactic elements comprising the steps of: selecting an alphabet containing at least lowercase letters, uppercase letters, and digits; selecting from the set of symbols, three primary symbols; calling primary value, a primary symbol used singly; calling ordinary symbols, all other symbols from the set of symbols; calling word, a chain of lowercase letters, coding natural languages nouns, adjectives, verbs, and adverbs; calling number, a chain of digits, coding natural whole numbers; calling elements the group consisting of primary values, words, numbers, and arrows; calling arrow, an element (the target) separated from either an element or an arrow (the source) by a change symbol; calling identifier, a chain of letters or digits beginning by an uppercase letter; calling lexical elements the group consisting of words, identifiers, and ordinary symbols; selecting variable symbols in the group consisting of uppercase letters used singly; calling syntactic elements the group consisting of symbols, words, numbers, identifiers, arrows, and variables.
 24. A computer implemented method as in claim 22, wherein a notation is assigned to each syntactic element that is a symbol and each said symbol has a symbol argument, further comprising the steps of: assigning a prefix notation for a symbol that is attached to the beginning of said symbol arguments; assigning a postfix notation for a symbol that is attached at the end of said symbol arguments; assigning a infix notation for a symbol that is inserted in the middle of said symbol arguments; and assigning a circumfix notation for a unary symbol that is placed around said symbol arguments.
 25. A computer implemented method as in claim 22, further comprising the step of assigning a sort of value to each syntactic element, comprising the steps of: selecting on said at least one computer sorts of value from the group consisting of truth-values and reality-values, sub-sorted into numerical, non numerical reality; Determining, by said at least one computer, if said Sort of Value is a Fixed value or Changing value; assigning a unique sort of value to each ordinary symbol; processing primary symbols as syntactic elements with polymorphic sorts, namely: used singly or with truth-valued syntactic elements which have said fixed values or said changing values; used with reality-valued syntactic elements which have fixed values or changing values.
 26. A computer implemented method as in claim 22, further comprising the step of assigning a whole number arity to each syntactic element, further comprising the steps of: assigning an arity equal to zero to elements, variables, and identifiers; assigning to each ordinary symbol, an arity equal to the number of authorized arguments; computing by said at least one computer the arity of primary symbols intangled inside or around other syntactic elements, in accordance with their position in regards to said syntactic elements.
 27. A computer implemented method as in claim 22, further comprising the steps of: assembling a unique symbol concatenated with only 0-arity syntactic elements, respecting the sort of value, arity and notation of said symbol and calling said unique symbol atomic; assembling a unique symbol concatenated with other well-formed syntactic elements, atomic or non-atomic, respecting the sort, arity and notation of said unique symbol and using parentheses to disambiguate the order of evaluation of syntactic elements and calling said unique symbol non-atomic; calling all other forms of syntactic elements “ill-formed”, and therefore “meaningless”, as their value is not computable; calling “the head”, the unique symbol of a well formed syntactic element, atomic or non-atomic, and calling “the body”, the rest of said well formed syntactic element; wherein the head and the body of a standalone element are the same; calling “the sort of value of a well formed syntactic element”, the sort of value of the head of that well formed syntactic element; calling “bound”, an occurrence of a variable, which is in the body of a quantifier or a function symbol in a well formed syntactic element; otherwise, the occurrence of that variable is called “free”; calling “ground”, a well formed syntactic element which contains no free variables; otherwise it is called “non-ground”; calling “literal”, a well formed syntactic element which contains only elements, and primary symbols; otherwise it is called “non-literal”; a literal is ground.
 28. A computer implemented method as in claim 22, wherein said well formed syntactic elements are typed as: instructions, which contain at least one symbol of definition, wherein said instructions are sub-typed as: injunctions, built on two formulas, surrounding the infix symbol of definition; definitions, built on an expression, a pre-condition, and an injunction, simple or multiple, separated by the infix symbol of definition; a definition is coded as a three-part pattern form; glossaries, which are ordered lists of definitions, separated by the infix symbol of definition; formulas, wherein formulas are sub-typed as expressions and terms and wherein said expressions are sub-typed as indication expressions and ordinary expressions; and said method is further comprising the steps of: equating, in said at least one computer, literal ordinary expressions either as arrangements with multiple primary symbols or primary values with only one Primary Symbol), wherein said terms are sub-typed as indication terms and ordinary terms; equating, in said at least one computer, literal ordinary terms either as packages, bunches or unitary terms.
 29. A computer implemented method as in claim 22, wherein each formal definition has a definition type selected from the group consisting of terminologies, assertions, theorems and questions and answers, wherein: a terminology is a non-ground definition with an atomic injunction, an assertion or anti-assertion is a ground definition with an atomic injunction, a theorem or anti-theorem is a non-ground definition with a non-atomic injunction, a question and answer is a definition with an unknown injunction, which must be computed by the present computer implemented method.
 30. A computer implemented method as in claim 22, wherein a defined lexical element is the unique lexical element that appears within the atomic indicative part of a three-part pattern coded terminology definition.
 31. A computer implemented method as in claim 22, further comprising the steps of: acquiring and ordering from a knowledge manager formal definitions having the same field specific semantic as their original natural language sentences to provide field specific distinctions; respecting the field specific distinctions, as each defined lexical element results from a laws of form calculus of distinction reasoning by said knowledge manager; formalizing said formal definitions following a three-part pattern where one part of said three-part pattern is the indication of the underlying distinction; and defining, in said at least one computer, said defined lexical element.
 32. A computer implemented method as in claim 22, further comprising the steps of: parsing and verifying, by said at least one computer, said formal glossaries and their formal definitions to infer the type of syntactic element they contain; normalizing primary expressions, for eliminating non-satisfiable sub-formulas while preserving their value, by applying repeatedly the laws of forms algebraic initials; providing a list of defined lexical elements contained in said formal definitions; producing, by said at least one computer, a minimal lexicon built from defined lexical elements that appear in the indicative part of a definition in said formal glossary.
 33. A computer implemented method as in claim 22, further comprising the steps of: retrieving, by said at least one computer, each assertion and theorem definition from said formal glossary; drawing consequences of each assertion and theorem definition, in accordance with an interpretation process having at least one critical algorithm; verifying consistency of each said assertion and theorem definition with existing terminology definitions, in accordance with the laws of form; providing, by said at least one computer, new derived assertion definitions, which are logical consequences of said assertion and theorem definition.
 34. A computer implemented method as in claim 22, further comprising the steps of: accepting from said actor, in said at least one computer, a question which is a set of formal texts containing at least one well formed syntactic element, wherein the value of said well-formed syntactic element is unknown; parsing and verifying the formal text of the question to infer the type of syntactic element it contains, and to produce formulas contained in the question; and initializing a rewriting area, in said at least one computer, with the formulas contained in the question.
 35. A computer implemented method as in claim 34, further comprising the steps of: retrieving, by said at least one computer, for each formula in the rewriting area, all matching formal definitions from formal glossaries, using algebraic mechanisms of unification and instantiation; eliminating redundant or inconsistent matching definitions to provide an optimized tree of applicable definitions, and its related current substitution; building, by said at least one computer, the tree of all applicable definitions, acquired from formal glossaries, to each sub-formula of the formulas in the rewriting area.
 36. A computer implemented method as in claim 34, wherein said interpretation process is further comprising the steps of: starting by translating each sub-formula of the formulas in the rewriting area, in accordance with the algebraic mechanisms of substitution and replacement, and continues until a literal formula appears; stopping by reducing said literal formula in the rewriting area, in accordance with the laws of form calculus of indications for computing its normal form, which is its value; wherein by laws of form, this value is unique.
 37. A computer implemented method as in claim 36, wherein said step of translating a sub-formula is further comprising the steps of: applying formal definitions from the tree of all applicable definitions, to said sub-formulas of said formula in said rewriting area; considering said formal definitions as conditional rewriting rules, to transform said formula while preserving its value; combining and comparing different results from a tree of all applicable definitions, to produce a unique meaningful value; coding the value of said formula, as computed in accordance with said interpretation process.
 38. A computer implemented method as in claim 37, wherein applying formal definitions is precisely defined by a combination of the pre-condition and Injunction mechanisms, namely: apply an injunction if a predetermined condition is true; do nothing if a predetermined condition is false; stop current transformation and transmit an unknownness value if a predetermined condition is undefined.
 39. A computer implemented method as in claim 22, further comprising the step of: Inserting laws of form algebraic Initials, position and & transposition, as theorem type definition in active glossary; initializing an active glossary with hard-coded definitions of string manipulations.
 40. A computer implemented method as in claim 39, wherein the list of hard coded functions (HCF) is comprising: concatenation of a string on the right side into a string; and updating a current substitution and rewriting area; de-concatenation of a string on the right side into a string, and a character; and updating the current substitution and the rewriting area; concatenation of a string on the left side into a string; and updating the current substitution and the rewriting area; de-concatenation of a string on the left side into a string and a character; and updating the current substitution and the rewriting area; generic equality of two formulas, including syntactic equality of strings, by unifying, valuating—by using FCA, and comparing syntactically their respective values, and updating the current substitution and the rewriting area; deactivation of a well formed syntactic element, which turns it into a mere and purely syntactical chain of symbols; and quantification of a formula by a variable, which develops that quantified formula by listing said variable on a words table, wherein a “for all” guantifier is developed as a generalized conjunction and a “there exists” guantifier is developed as a generalized disjunction.
 41. A computer implemented method as in claim 22, wherein said critical algorithm is selected from the group consisting of formula calculation algorithm (FCA), add definition algorithm (ADA) and equation resolution algorithm (ERA).
 42. A computer implemented method as in claim 22, further comprising the steps of: providing an answer to said actor as the meaningful value of a syntactic element, if said syntactic element is not meaningless.
 43. A computer implemented method as in claim 22, further comprising the steps of: saving, in said at least one computer, said consistent ordered set of formal definitions, as a certified formal glossary.
 44. A computer implemented method as in claim 22, further comprising the steps of: processing a certified formal glossary as a formal text using a self-referential glossary; certifying compliance of said certified formal glossary to provide a certified and consistent formal glossary; and providing an initial intelligent glossary, and its related minimal lexicon, from said certified and consistent formal glossary.
 45. A system for verifying, implementing and using a semantic system of intelligent glossaries, said system comprising: at least one computer comprising: an interpretation module having an initialization module, and at least one critical algorithm, wherein said interpretation module provides a value for questions, which are set of formal texts containing at least one well-formed syntactical element; a parsing module which processes texts of formal glossaries and formal questions; an add definition module for verifying a formal glossary, definition by definition, and for certifying compliance and consistency of said glossary; at least one active glossary for storing current glossaries of the whole system; a current substitution initialized with the an empty set and updated after at least one translation; a rewriting area for computing on formulas, from the initial formal text of a question, up to its meaningful value; a words table for storing natural language words and the name of their container glossary; a viewer module for editing glossaries and questions, and for interacting with actors; and a file update module for updating glossaries having at least one definition and associated interpretation from said interpretation module.
 46. A system as in claim 45, wherein said initialization module provides system localization services and data structures initialization.
 47. A system as in claim 45, wherein said parsing module transforms formal texts into lexical trees, containing well formed syntactic elements and their properties; and infers automatically the lexical element type of each well-formed syntactic element in said lexical trees.
 48. A system as in claim 45, wherein said translation module provides an interpretation for each lexical tree corresponding to a formal text; provides a graph of dependencies between nodes of said lexical trees during computation to detect cycles of computation; provides numbering of variable symbols to avoid collision between variables of a question and variables of a definition, or variables of deactivated sub-formulas of the same question; provides a cache pooling collection for memorizing previously computed formulas and their unique value, to optimize computation algorithms by retrieving values by rapid hash-coding access mechanisms.
 49. A system as in claim 45, wherein said at least one critical algorithm is selected from the group consisting of hard coded functions (HCF), formulas calculation algorithm (FCA), add definition algorithm (ADA), and equation resolution algorithm (ERA).
 50. A system as in claim 45, further comprising: an intelligent glossary containing the ordered set of definitions for said lexical elements.
 51. A system as in claim 45, further comprising: at least one minimal lexicon generated from said intelligent glossary. 